Question

(4 points) Smart Driver Driving School has many branches across provinces. In a province different from the one in problem 1, the teaching committee at the provincial branch randomly assigned half of their 5000 students enrolled this year to receive the conventional teaching method and the remaining half to receive the new teaching method. In a random sample of 100 students who received the conventional teaching method, 79 passed the road test. In another random sample of 100 students who received the new teaching method, 84 passed the road test. The committee would like to use the sample data to test if the two teaching methods have different passing rates. Let Pc and PN be the true passing rates of the conventional and the new teaching methods, respectively. Part i) What are the appropriate null and alternative hypotheses? O A. Ho: Pc - PN = 0 and HA: PC - PN +0 B. HPN = 0.79 and HA: PN +0.79 c. H : PC - PN = 0 and HA : PC - PN > 0 D. H : Pc - PN = 0 and HA : PC - PN <0 Part ii) The committee decides to perform the hypothesis test at 10% significance level. Which of the following is/are true? (Check all that apply.) A. The probability of committing the Type I error is 10%. B. The probability of committing the Type Il error is 90% C. The Type I error is 10%. OD. There is 10% chance to reject the null hypothesis. E. The Type Il error is 90% OF. There is 10% chance that the null hypothesis is true. G. None of the above. Part iii) Which of the following assumptions and conditions are needed to carry out the hypothesis test? CHECK ALL THAT APPLY A. The counts of successes and failures are each 10 or more in both samples B. The counts of successes and failures are each 5 or more in both samples C. The two random samples of students are independent. D. The variable whether a student passes or not follows the Normal model. E. None of the above. Part iv) Construct a "Large-Sample" 95% confidence interval for the difference in the true passing rates (expressed as proportions) between the conventional and new teaching methods: ) [For this question, use the methods described in lecture - do not use R prop.test(). You must use at least four decimal places for all intermediate 95% confidence interval:( calculations and your final answer]

Answer 1

Given nic 100 XI 79 na 100 X2 = 84 7.9 100 1 - = - 76. oito Beauty - 34 0.84 0.79 100 Ho.. PC- Pro vis HA PC- PHI 0 xe 10% = 0.01 Probability of committing Typer 2 ensor is 10%. Tu ) - The counts of successes and failures are each 10 or more in both samples. - the Count The Tho random s of students are independant. 95%. Contidance interval for the difference in true passing rate Co-P2 + 2x12x J Pict-p.) Pacife ni nz (0.79-0.86) + 20.025 x 10.79X0.21 0.8480.16 i 100 -0.0.5 + 1.968 0.055 -0.05 + 0.1078 - 0.1578 LPI-P2 < 0.0578